id: 06546542
dt: j
an: 2016b.00581
au: Pritchard, Chris
ti: A square peg in a round hole.
so: Math. Sch. (Leicester) 39, No. 5, 11-13 (2010).
py: 2010
pu: Mathematical Association (MA), Leicester
la: EN
cc: G40 G60 G70 D50
ut: plane geometry; area; circles; squares; proportion; Pythagorean theorem;
nesting; ratio; equal excess and defect; trigonometry; coordinate
geometry; straight line; analytic geometry; rich task; non-routine
problems; open-ended problems
ci:
li:
ab: From the text: Which fits better, a square peg in a round hole or a round
peg in a square hole? This style of problem is attractive. It’s
stated in very simple terms, slick even, but there’s a good bit of
mathematics behind the scenes waiting to be discovered. It exhibits
some characteristics of a ‘rich task’. It can certainly be extended
in many different directions and to various levels of complexity and
could be used as a starting point for an investigation or else prompt
guided discovery activities to reveal many of the mathematical methods
that students need to learn from KS3 upwards to university. You might
argue, quite reasonably, that the question is not very well defined.
What is the intended meaning? Well, this is what I want students to
explore: Consider a square drawn inside a circle. What proportion of
the circle’s area is taken up by the square? Now consider a circle
drawn inside a square. What proportion of the square’s area is taken
up by the circle? And hence, which fits the better?
rv: